Yes, trying to localize/isolate the problem by trial-and-listen is the way to go.

Does it click (or whatever) when I am pedalling?
When I am coasting?
In certain gears?
In a certain chainring?
In the same gear on either of the chainrings?
Are my laces clicking on my crank?
What if I brake and release, do it stop the sound? (Possible brake rub.)
Is my lock on my rack and rubbing on something?

If it goes psssst! it's a flat tire.

After going CRAZY for weeks I finally figured out that the spoke-protector disk on my bike is vibrating and making awful sounds. I got off the bike and moved the disk with my fingers. Sure enough, that's what was making the sound. It's still vibrating but now I know what it is and it doesn't drive me crazy anymore. I'll get it removed as soon as possible. (I don't want to break it to remove it.)